Fibonacci sequence

The Fibonacci sequence is a mathematical pattern where each number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34... Named after medieval mathematician Leonardo Fibonacci, it emerges unexpectedly throughout nature and art, making it one of mathematics' most enchanting discoveries.

The sequence appears in spirals of sunflower seeds, branching patterns of trees, and proportions of seashells. This prevalence hints at deep organizing principles in how living systems evolved. The ratio between consecutive Fibonacci numbers approaches the Golden ratio, a proportion that architects and artists have long found aesthetically compelling.

Beyond nature, Fibonacci numbers unlock patterns in rings, optimize computer algorithms, and model temporal processes across domains. Visualizing these sequences reveals their recursive beauty—each term depends only on what came before, a principle mirrored in loops throughout systems theory.

The sequence connects mathematics to design, information structures, and even financial market analysis. Its simplicity hides profound depth: a humble rule generating infinite complexity.

Related

Golden ratio, Spirals, Leonardo Fibonacci, Recursion, Pattern recognition, Mathematical modeling